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Downloads
Views
Date
Relevance
Modeling Scenario
333
views
160
downloads
0
comments
3-102-SpringMassDamped-ModelingScenario
Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.
frequency
mass
oscillation
stiffness
spring constant
spring\
damped
Single Degree of Freedom System
coefficient
Modeling Scenario
319
views
191
downloads
0
comments
3-010-EnergyInSpringMassSystem-ModlingScenario
As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
energy
mass-spring system
kinetic energy
potential energy
total energy
Article or Presentation
842
views
410
downloads
0
comments
2020-TeachingModule-SpringDesignToMeetSpecsAtMinimumCosts
We discuss a Modeling Scenario in which students are asked to design a spring mass system at minimum costs give relative costs of features of the spring.
module
optimization
spring mass
mass
spring\
cost
Teaching Module
minimal cost
Modeling Scenario
389
views
418
downloads
0
comments
3-001-SpringMassDataAnalysis-ModelingScenario
We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass configuration and estimation of parameters are the core.
data
damping
spring-mass system
Newton's Second Law of Motion
spring constant
Hooke's Law
Modeling Scenario
332
views
393
downloads
0
comments
5-040-TunedMassDampers-PartII-ModelingScenario
Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a spring-mass-dashpot with stiffness replacing spring...
structure
resistance
spring-mass-dashpot
earthquake
vibration
control
damping
tuned mass damper
stiffness
reduction of vibration
Modeling Scenario
213
views
141
downloads
0
comments
3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.
mass
undamped
Free Body Diagram
springs
two springs
oscil
lation
spring constant
fixed ends
Modeling Scenario
268
views
143
downloads
0
comments
3-091-SpringModeling-ModelingScenario
In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data.
data
laboratory
LoggerPro
Vernier
mass-spring system
model validation
empirical model
theoretical model
Potential Scenario
170
views
45
downloads
0
comments
2013-Boscolo-Stellato-Undergraduate study of harmonic and parametric motion of a simple spring-mass system from motion waveforms
In this paper, we describe a laboratory exercise that caters to beginning students while giving those with more background an opportunity to explore more complex aspects of the motion.
laboratory
experiment
spring mass
air friction
apparatus
waveforms
Potential Scenario
165
views
56
downloads
0
comments
2012-Rusinko-Swan-Agent-Based Fabric Modeling Using Differential Equations
We use an agent-based modeling software, NetLogo, to simulate fabric drape by applying a modified mass spring system.
NetLogo
spring mass
agent-based
draping
yarn
fabric
Modeling Scenario
242
views
166
downloads
0
comments
3-031-SpringCost-ModelingScenario
We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and cost.
design
unit cost
spring constant
static equilibrium
spring masss dashpot
Potential Scenario
161
views
72
downloads
0
comments
2017-Guy-Bart_Stan-Modelling in Biology
This is a very rich set of notes, rich in examples and ideas for modeling. In almost all cases after a model is introduced in real context there is attention to stability analysis.
spring mass
bifurcation
mass action
limit cycles
Modeling Scenario
537
views
1390
downloads
0
comments
5-040-TunedMassDamper-Part-I-Modeling Scenario
We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original structure as a spring-mass-dashpot system.
structure
spring-mass-dashpot
spring mass
earthquake
vibration
tuned mass tuner
restoring force
control
dampe
Modeling Scenario
268
views
418
downloads
0
comments
3-090-OneSpringMass-ModelingScenario
We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...
undamped
sum of square errors
mass spring
Hooke's Law
oscilation
least-squares approximation
Potential Scenario
122
views
62
downloads
0
comments
2003-Fay-Graham-Coupled spring equations
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
spring mass
oscillation
Hooke's Law
coupled springs
periodic
forcing function
phase portrait
Potential Scenario
139
views
79
downloads
0
comments
2003-Fay-Graham-Coupled spring equations
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
mass
oscillation
spring\
coupled springs
periodic
fporcing
Modeling Scenario
243
views
123
downloads
0
comments
3-040-FirstPassageTime-ModelingScenario
We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.
oscillator
damped
underdamped
first passage
first passage time
spring mash dashpot
Modeling Scenario
259
views
208
downloads
0
comments
3-105-FrequencyResponse-ModelingScenario
We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.
transient dynamics
circuit
spring mass
driver
frequency response
amplitude
steady state
Potential Scenario
157
views
78
downloads
0
comments
2016-Pennell-Avitabile-White-Engineering Applications Differential Equations
General discussion of an engineering based differential equations course with examples from RC Circuit, mass spring dashpot.
circuit
voltage
capacitor
nondimensionalization
Modeling Scenario
748
views
753
downloads
0
comments
3-034-CarSuspension-ModelingScenario
We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.
design
spring-mass-dashpot
spring constant
underdamping
car suspension
suspension tolerance
static equilibrium
Potential Scenario
369
views
97
downloads
0
comments
2017-Varanis-Mereles-Mathematical Model of a Vehicle Crash A Case Study
The model proposed in this paper allows one to obtain the parameters of the system, and then compare them with the ones obtained experimentally to test the suitability of the model with the vehicle crash.
case study
Runge-Kutta
spring mass damper
vehicle crash
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